period

Period detection of chaotic sequences

represented with finite precision

DescriptionThe Period
class implements in C++ the sliding window algorithm in order to find periods
in a chaotic sequence represented with finite precision. The class is
templated so that the precision can be externally specified. The
following finite representations are known to be supported:

floating point (see IEEE754 class) single precision (32 bits)

floating point double precision (64 bits)

fixed point (see TFixed class)

The chaotic sequences are generated using generators of the form x_n = f(x_{n-1}), where f:[0,1]->[0,1] is the chaotic map. The following chaotic maps are implemented:

logistic map

tent map

Chebyshev polynomials

skew tent map

Bernoulli map (a.k.a. r-adic map)

piece-wise linear chaotic map

Other chaotic maps could be implemented by modifying Period<T,U>::chaotic_map function.For usage examples see period.cpp, scan_interval.cpp, show_seq.cpp or bin_stream.cpp.